Epitaxial thin films of inorganic single crystals can be grown on single-crystal substrates with a variety of different solution chemistries. This review emphasizes chemical solution deposition, in which a solution is used to deposit a layer of precursor molecules that decompose to low-density, polycrystalline films during heating. Ways to control film cracking during deposition and heat treatment and why many precursors synthesize metastable crystalline structures are discussed, and the different mechanisms that convert the polycrystalline film into a single crystal are reviewed. Hydrothermal epitaxy, in which single crystal thin films are directly synthesized on templating substrates in an aqueous solution at temperatures <150°C, is also discussed.